abstract: Almost 30 years ago Amgren wrote his by now famous "Big regularity paper" on the partial regularity of higher codimension minimizing currents.
In this course I present some recent progress in collaboration with C. De Lellis in the direction of a new, simpler derivation of some of Almgren's results, recast in a more manageable framework.
I will in particular talk about the theory of multiple valued minimizing functions and the approximation of minimal currents. Finally, time permitting, I will also discuss some of the issues on Almgren's center manifold construction.